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Van der Waals constant b of helium is 24 mL mol^-1. Find molecular diameter of helium.
(1) 1.335$\times$10^-10 cm
(2) 1.335$\times$10^-8 cm
(3) 2.67$\times$10^-8 cm
(4) 4.34$\times$10^-8 cm

At low pressure, if RT=$2\sqrt{a.P}$, then the volume occupied by a real gas is :
(1) $\frac{2\mathrm{RT}}{\mathrm{P}}$
(2) $\frac{2\mathrm{P}}{\mathrm{RT}}$
(3) $\frac{RT}{2P}$
(4) $\frac{2\mathrm{RT}}{P}$

At low pressure, van der wall's equation is written as $\left(P+\frac{a}{V^2}\right)V=RT$. The compressibility factor is then equal to:
(1) $\left(1-\frac{a}{RTV}\right)$
(2) $\left(1-\frac{RTV}{a}\right)$
(3) $\left(1+\frac{a}{RTV}\right)$
(4) $\left(1+\frac{RTV}{a}\right)$

The Van der waal's equation of law of corresponding states for q mole of gas is :
(1) $\left(P_r+\frac{3}{{V_r}^2}\right)(3V_r-1)=8T_r$
(2) $\left(P_r-\frac{3}{{V_r}^2}\right)(3V_r-1)=8 T_r$
(3) $\left(P_r+\frac{3}{{V_r}^2}\right)(3V_r+1)=8 \mathrm{\pi }{T}_r$
(4) $\left(P_r+\frac{3}{{V_r}^2}\right)(3V_r+1)=8$

Calculate the volume occupied by 16 gram O₂ at 300 K and 8.31 MPa if $\frac{{\mathrm{P}}_{\mathrm{C}}{\mathrm{V}}_{\mathrm{C}}}{{\mathrm{RT}}_{\mathrm{C}}}=3/8$ and$\frac{P_r{V}_r}{T_r}=2.21$ (Give : R=8.314 MPa/K-mol)
(1) 125.31 mL
(2) 124.31 mL
(3) 248..62 mL
(4) None of these

For a real gas (mol. mass = 60) if density at critical point is 0.80 g/cm³ and its $T_C=\frac{4\times {10}^5}{821}K,$ then van der Waal's constant a (in atm L² mol^-2) is
(1) 0.3375
(2) 3.375
(3) 1.68
(4) 0.025

The van der Waal's constant 'b' of a gas is $4\mathrm{\pi }\times {10}^{-4} \mathrm{L}/\mathrm{mol}$. How near can the centres of the two molecules approach each other ? $\left[Use: N_A=6\times {10}^{23}\right]$
(1) 10^-7 m
(2) 10^-10 m
(3) 5$\times$10^-11 m
(4) 5$\times$10^-9 m

Vander Waal's gas equation can be reduced to virial equation and virial equation (in terms of volume) is Z = $\mathrm{A}+\frac{\mathrm{B}}{{\mathrm{V}}_{\mathrm{m}}}+\frac{\mathrm{C}}{{{\mathrm{V}}_{\mathrm{m}}}^2}+....$ where A= first virial coefficient, B=second virial coefficient of Hg(g) is 625 ${(cm}^{}$²/mol)2. What volume is available for movement of 10 moles He(g) atoms present in 50 L vessel ?
(1) 49.75 L
(2) 49.25 L
(3) 25 L
(4) 50 L

If the slope of 'Z' (compressibility factor) v/s 'P' curve is constant (slope=$\frac{\mathrm{\pi }}{492.6}at{m}^{-1}$) at a particular temperature (300 K) and very high pressure, then calculate diameter of the molecules.
(Given : ${\mathrm{N}}_{\mathrm{A}}=6.0\times {10}^{23}$, R=0.0821 atm. lit $mo{l}^{-1} K^{-1}$)
(1) $7.5 \stackrel{0}{A}$
(2) $5\stackrel{0}{ A}$
(3) $2.5\stackrel{0}{ A}$
(4) $1.25\stackrel{0}{ A}$

For two samples A and B of ideal gas following curve is plotted between n vs V (volume of container) at 16.42 atm pressure as follows, then temperature of A and B respectively are:

(1) $\frac{200}{\sqrt{3}}K, 200\sqrt{3}$K
(2) $\frac{200}{\sqrt{3}}°C, \left(200\sqrt{3}\right)°C$
(3) $200\sqrt{3}K, \frac{200}{\sqrt{3}} K$
(4) $200 K, \frac{\sqrt{3}}{200} K$

What is the density of wet air with 75% relative humidity at 1 atm and 300 K? Given : vapour pressure of H₂O is 30 torr and average molar mass of air is 29 g mol^-1
(1) 1.614 g/L
(2) 0.96 g/L
(3) 1.06 g/L
(4) 1.164 g/L

7 moles of a tetra-atomic non-linear gas 'A' at 10 atm and T K are mixed with 6 moles of another gas B at $\frac{T}{3} K$ and 5 atm in a closed, rigid vessel without energy transfer with surroundings. If final temperature of mixture was $\frac{5T}{6}K$, then gas B is? (Assuming all modes of energy are active)
(1) Monoatomic
(2) Diatomic
(3) triatomic
(4) tetra atomic

Three closed rigid vessels A, B and C without energy transfer with surroundings, which initially contain three different gases at different temperatures are connected by tube of  negligible volume. The vessel A contain 2 mole Ne gas, at 300 K, vessel 'B' contain 2 mole SO₂ gas at 400 K and vessel 'C' contain 3 mole CO₂ gas at temperature 500 K. What is the final pressure (in atm) attained by gases when all valves of connecting three vessels are opened and additional 15.6 kcal heat supplied to vessel through valve. The volume of A, B and C vessel is 2, 2 and 3 litre respectively
(Given : R = 2 calorie/mol-K; C_v(Ne)=3/2 R, C_v (CO)=5/2 R and C_v(SO₂)=3R)

(1) 73.89 atm
(2) 67.31 atm
(3) 80 atm
(4) none of these

Gas molecules each of mass 10^-26 kg are taken in a container of volume 1 dm³. The root mean square speed of gas molecules is 1 km sec^-1. What is the temperature of gas molecules.
(Given : N_A=6$\times {10}^{23}; R=8 J/mol.K)$
(1) 298 K
(2) 25 K
(3) 241 K
(4) 2500 K

If one mole each of a monoatomic and diatomic gases are mixed at low temperature then C_p/C_v ratio for the mixture is :
(1) 1.40
(2) 1.428
(3) 1.5
(4) 1.33

The compressibility factor for a real gas at high pressure is:
(1) 1
(2) $1+\frac{Pb}{RT}$
(3) $1-\frac{Pb}{RT}$
(4) $1+\frac{RT}{Pb}$

At 273 K temp. and 9 atm pressure, the compressibility for a gas is 0.9. The volume of 1 milli-moles of gas at this temperature and pressure is:
(1) 2.24 litre
(2) 0.020 mL
(3) 2.24 mL
(4) 22.4 mL

The compressibility factor for nitrogen at 330 K and 800 atm is 1.90 and at 570 K and 200 atm is 1.10. A certain mass of N₂ occupies a volume of 1 dm³ at 330 K and 800 atm. Calculate volume occupied by same quantity of N2 gas at 570 K and 200 atm:
(1) 1 L
(2) 2 L
(3) 3 L
(4) 4 L

What is the compressibility factor (Z) for 0.02 mole of  van der Waal's gas at pressure of 0.1 atm. Assume the size of gas molecules is negligible.
Given: RT=20 L atm mol^-1 and a=1000 atm L² mol^-1
(1) 2
(2) 1
(3) 0.02
(4) 0.5